Triangles
(B A C
and
B F C)
on the same base and between the same parallels are equal.

Through the point
B draw
B E
parallel to
C A,
and draw
B D
parallel to
C F,
and produce
A F
to meet these lines at
E
and
D.
ABCDEF
The figures
B E A C
and
B D F C
are parallelograms on the same base
B C
and between the same parallels, and therefore,
(XXXV)
equal; and the triangles
B A C
and
B F C
are their halves
(XXXIV),
and therefore also equal.